Diblock copolymers of poly(ethylene glycol) (PEG) and biodegradable polycarbonate functionalized with GSH-sensitive disulfide bonds and pH-responsive carboxylic acid groups were synthesized via organocatalytic ring-opening polymerization of functional cyclic carbonates with PEG having different molecular weights as macroinitiators. These narrowly-dispersed polymers had predictable molecular weights, and were used to load doxorubicin (DOX) into micelles primarily through ionic interactions. The DOX-loaded micelles exhibited the requisite small particle size (<100 nm), narrow size distribution and high drug loading capacity. When exposed to endolysosomal pH of 5.0, drug release was accelerated by at least two-fold. The introduction of GSH further expedited DOX release. Effective DOX release enhanced cytotoxicity against cancer cells. More importantly, the DOX-loaded micelles with the optimized composition showed excellent antitumor efficacy in nude mice bearing BT-474 xenografts without inducing toxicity. These pH and redox dual-responsive micelles have the potential as delivery carriers to maximize the therapeutic effect of anticancer drugs.